Boosting quantum artificial intelligence models

ABSTRACT

Systems, computer-implemented methods, and computer program products that can facilitate a classical and quantum ensemble artificial intelligence model are described. According to an embodiment, a system can comprise a memory that stores computer executable components and a processor that executes the computer executable components stored in the memory. The computer executable components can comprise an ensemble component that generates an ensemble artificial intelligence model comprising a classical artificial intelligence model and a quantum artificial intelligence model. The computer executable components can further comprise a score component that computes probability scores of a dataset based on the ensemble artificial intelligence model.

BACKGROUND

The subject disclosure relates to artificial intelligence models, andmore specifically, to boosting quantum artificial intelligence models.

SUMMARY

The following presents a summary to provide a basic understanding of oneor more embodiments of the invention. This summary is not intended toidentify key or critical elements, or delineate any scope of theparticular embodiments or any scope of the claims. Its sole purpose isto present concepts in a simplified form as a prelude to the moredetailed description that is presented later. In one or more embodimentsdescribed herein, devices, systems, computer-implemented methods, and/orcomputer program products that can facilitate a classical and quantumensemble artificial intelligence model are described.

According to an embodiment, a system can comprise a memory that storescomputer executable components and a processor that executes thecomputer executable components stored in the memory. The computerexecutable components can comprise an ensemble component that generatesan ensemble artificial intelligence model comprising a classicalartificial intelligence model and a quantum artificial intelligencemodel. The computer executable components can further comprise a scorecomponent that computes probability scores of a dataset based on theensemble artificial intelligence model.

According to another embodiment, a computer-implemented method cancomprise generating, by a system operatively coupled to a processor, anensemble artificial intelligence model comprising a classical artificialintelligence model and a quantum artificial intelligence model. Thecomputer-implemented method can further comprise computing, by thesystem, probability scores of a dataset based on the ensemble artificialintelligence model.

According to another embodiment, a computer program product that canfacilitate a classical and quantum ensemble artificial intelligencemodel. The computer program product can comprise a computer readablestorage medium having program instructions embodied therewith, theprogram instructions can be executable by a processor to cause theprocessor to generate, by the processor, an ensemble artificialintelligence model comprising a classical artificial intelligence modeland a quantum artificial intelligence model. The program instructionscan be further executable by the processor to cause the processor tocompute, by the system, probability scores of a dataset based on theensemble artificial intelligence model.

DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a block diagram of an example, non-limiting systemthat can facilitate a classical and quantum ensemble artificialintelligence (AI) model in accordance with one or more embodimentsdescribed herein.

FIG. 2 illustrates a block diagram of an example, non-limiting systemthat can facilitate a classical and quantum ensemble artificialintelligence (AI) model in accordance with one or more embodimentsdescribed herein.

FIG. 3 illustrates an example, non-limiting algorithm that canfacilitate a classical and quantum ensemble artificial intelligence (AI)model in accordance with one or more embodiments described herein.

FIG. 4 illustrates an example, non-limiting system that can facilitate aclassical and quantum ensemble artificial intelligence (AI) model inaccordance with one or more embodiments described herein.

FIG. 5 illustrates an example, non-limiting system that can facilitate aclassical and quantum ensemble artificial intelligence (AI) model inaccordance with one or more embodiments described herein.

FIG. 6A illustrates an example, non-limiting system that can facilitatea classical and quantum ensemble artificial intelligence (AI) model inaccordance with one or more embodiments described herein.

FIG. 6B illustrates an example, non-limiting system that can facilitatea classical and quantum ensemble artificial intelligence (AI) model inaccordance with one or more embodiments described herein.

FIG. 6C illustrates an example, non-limiting quantum feature map thatcan facilitate a classical and quantum ensemble artificial intelligence(AI) model in accordance with one or more embodiments described herein.

FIGS. 7A, 7B, 7C, and 7D illustrate example, non-limiting scripts thatcan facilitate a classical and quantum ensemble artificial intelligence(AI) model in accordance with one or more embodiments described herein.

FIG. 8A illustrates an example, non-limiting table that can facilitate aclassical and quantum ensemble artificial intelligence (AI) model inaccordance with one or more embodiments described herein.

FIGS. 8B and 8C illustrate example, non-limiting matrices that canfacilitate a classical and quantum ensemble artificial intelligence (AI)model in accordance with one or more embodiments described herein.

FIG. 8D illustrates an example, non-limiting plot that can facilitate aclassical and quantum ensemble artificial intelligence (AI) model inaccordance with one or more embodiments described herein.

FIG. 9A illustrates a flow diagram of an example, non-limitingcomputer-implemented method that can facilitate a classical and quantumensemble artificial intelligence (AI) model in accordance with one ormore embodiments described herein.

FIG. 9B illustrates a flow diagram of an example, non-limitingcomputer-implemented method that can facilitate a classical and quantumensemble artificial intelligence (AI) model in accordance with one ormore embodiments described herein.

FIG. 10 illustrates a block diagram of an example, non-limitingoperating environment in which one or more embodiments described hereincan be facilitated.

DETAILED DESCRIPTION

The following detailed description is merely illustrative and is notintended to limit embodiments and/or application or uses of embodiments.Furthermore, there is no intention to be bound by any expressed orimplied information presented in the preceding Background or Summarysections, or in the Detailed Description section.

One or more embodiments are now described with reference to thedrawings, wherein like referenced numerals are used to refer to likeelements throughout. In the following description, for purposes ofexplanation, numerous specific details are set forth in order to providea more thorough understanding of the one or more embodiments. It isevident, however, in various cases, that the one or more embodiments canbe practiced without these specific details. It is noted that thedrawings of the present application are provided for illustrativepurposes only and, as such, the drawings are not drawn to scale.

Quantum computing is generally the use of quantum-mechanical phenomenafor the purpose of performing computing and information processingfunctions. Quantum computing can be viewed in contrast to classicalcomputing, which generally operates on binary values with transistors.That is, while classical computers can operate on bit values that areeither 0 or 1, quantum computers operate on quantum bits that comprisesuperpositions of both 0 and 1, can entangle multiple quantum bits(qubits), and use interference.

Classical artificial intelligence (AI) and/or machine learning (ML)systems and/or techniques scale well to large datasets. However, thereare limitations to scaling quantum artificial intelligence (AI) and/orquantum machine learning (ML) systems and/or techniques on near termquantum computers primarily due to the time it takes to load data,number of qubits, and/or depth of quantum circuit. As referenced herein,an artificial intelligence (AI) model can comprise a machine learning(ML) model.

FIG. 1 illustrates a block diagram of an example, non-limiting system100 that can facilitate a classical and quantum ensemble artificialintelligence (AI) model in accordance with one or more embodimentsdescribed herein. According to several embodiments, system 100 cancomprise an ensemble system 102. In some embodiments, ensemble system102 can comprise a memory 104, a processor 106, an ensemble component108, a score component 110, and/or a bus 112.

It should be appreciated that the embodiments of the subject disclosuredepicted in various figures disclosed herein are for illustration only,and as such, the architecture of such embodiments are not limited to thesystems, devices, and/or components depicted therein. For example, insome embodiments, system 100 and/or ensemble system 102 can furthercomprise various computer and/or computing-based elements describedherein with reference to operating environment 1000 and FIG. 10 . Inseveral embodiments, such computer and/or computing-based elements canbe used in connection with implementing one or more of the systems,devices, components, and/or computer-implemented operations shown anddescribed in connection with FIG. 1 or other figures disclosed herein.

According to multiple embodiments, memory 104 can store one or morecomputer and/or machine readable, writable, and/or executable componentsand/or instructions that, when executed by processor 106, can facilitateperformance of operations defined by the executable component(s) and/orinstruction(s). For example, memory 104 can store computer and/ormachine readable, writable, and/or executable components and/orinstructions that, when executed by processor 106, can facilitateexecution of the various functions described herein relating to ensemblesystem 102, ensemble component 108, score component 110, and/or anothercomponent associated with system 100 and/or ensemble system 102, asdescribed herein with or without reference to the various figures of thesubject disclosure.

In some embodiments, memory 104 can comprise volatile memory (e.g.,random access memory (RAM), static RAM (SRAM), dynamic RAM (DRAM), etc.)and/or non-volatile memory (e.g., read only memory (ROM), programmableROM (PROM), electrically programmable ROM (EPROM), electrically erasableprogrammable ROM (EEPROM), etc.) that can employ one or more memoryarchitectures. Further examples of memory 104 are described below withreference to system memory 1016 and FIG. 10 . Such examples of memory104 can be employed to implement any embodiments of the subjectdisclosure.

According to multiple embodiments, processor 106 can comprise one ormore types of processors and/or electronic circuitry that can implementone or more computer and/or machine readable, writable, and/orexecutable components and/or instructions that can be stored on memory104. For example, processor 106 can perform various operations that canbe specified by such computer and/or machine readable, writable, and/orexecutable components and/or instructions including, but not limited to,logic, control, input/output (I/O), arithmetic, and/or the like. In someembodiments, processor 106 can comprise one or more central processingunit, multi-core processor, microprocessor, dual microprocessors,microcontroller, System on a Chip (SOC), array processor, vectorprocessor, and/or another type of processor. Further examples ofprocessor 106 are described below with reference to processing unit 1014and FIG. 10 . Such examples of processor 106 can be employed toimplement any embodiments of the subject disclosure.

In some embodiments, ensemble system 102, memory 104, processor 106,ensemble component 108, score component 110, and/or another component ofensemble system 102 as described herein can be communicatively,electrically, and/or operatively coupled to one another via a bus 112 toperform functions of system 100, ensemble system 102, and/or anycomponents coupled therewith. In several embodiments, bus 112 cancomprise one or more memory bus, memory controller, peripheral bus,external bus, local bus, and/or another type of bus that can employvarious bus architectures. Further examples of bus 112 are describedbelow with reference to system bus 1018 and FIG. 10 . Such examples ofbus 112 can be employed to implement any embodiments of the subjectdisclosure.

In some embodiments, ensemble system 102 can comprise any type ofcomponent, machine, device, facility, apparatus, and/or instrument thatcomprises a processor and/or can be capable of effective and/oroperative communication with a wired and/or wireless network. All suchembodiments are envisioned. For example, ensemble system 102 cancomprise a server device, a computing device, a general-purposecomputer, a special-purpose computer, a quantum computing device (e.g.,a quantum computer, a quantum processor, etc.), a tablet computingdevice, a handheld device, a server class computing machine and/ordatabase, a laptop computer, a notebook computer, a desktop computer, acell phone, a smart phone, a consumer appliance and/or instrumentation,an industrial and/or commercial device, a digital assistant, amultimedia Internet enabled phone, a multimedia players, and/or anothertype of device.

In some embodiments, ensemble system 102 can be coupled (e.g.,communicatively, electrically, operatively, etc.) to one or moreexternal systems, sources, and/or devices (e.g., computing devices,communication devices, etc.) via a data cable (e.g., coaxial cable,High-Definition Multimedia Interface (HDMI), recommended standard (RS)232, Ethernet cable, etc.). In some embodiments, ensemble system 102 canbe coupled (e.g., communicatively, electrically, operatively, etc.) toone or more external systems, sources, and/or devices (e.g., computingdevices, communication devices, etc.) via a network.

According to multiple embodiments, such a network can comprise wired andwireless networks, including, but not limited to, a cellular network, awide area network (WAN) (e.g., the Internet) or a local area network(LAN). For example, ensemble system 102 can communicate with one or moreexternal systems, sources, and/or devices, for instance, computingdevices (and vice versa) using virtually any desired wired or wirelesstechnology, including but not limited to: wireless fidelity (Wi-Fi),global system for mobile communications (GSM), universal mobiletelecommunications system (UMTS), worldwide interoperability formicrowave access (WiMAX), enhanced general packet radio service(enhanced GPRS), third generation partnership project (3GPP) long termevolution (LTE), third generation partnership project 2 (3GPP2) ultramobile broadband (UMB), high speed packet access (HSPA), Zigbee andother 802.XX wireless technologies and/or legacy telecommunicationtechnologies, BLUETOOTH®, Session Initiation Protocol (SIP), ZIGBEE®,RF4CE protocol, WirelessHART protocol, 6LoWPAN (IPv6 over Low powerWireless Area Networks), Z-Wave, an ANT, an ultra-wideband (UWB)standard protocol, and/or other proprietary and non-proprietarycommunication protocols. In such an example, ensemble system 102 canthus include hardware (e.g., a central processing unit (CPU), atransceiver, a decoder), software (e.g., a set of threads, a set ofprocesses, software in execution) or a combination of hardware andsoftware that facilitates communicating information between ensemblesystem 102 and external systems, sources, and/or devices (e.g.,computing devices, communication devices, etc.).

According to multiple embodiments, ensemble system 102 can comprise oneor more computer and/or machine readable, writable, and/or executablecomponents and/or instructions that, when executed by processor 106, canfacilitate performance of operations defined by such component(s) and/orinstruction(s). Further, in numerous embodiments, any componentassociated with ensemble system 102, as described herein with or withoutreference to the various figures of the subject disclosure, can compriseone or more computer and/or machine readable, writable, and/orexecutable components and/or instructions that, when executed byprocessor 106, can facilitate performance of operations defined by suchcomponent(s) and/or instruction(s). For example, ensemble component 108,score component 110, and/or any other components associated withensemble system 102 as disclosed herein (e.g., communicatively,electronically, and/or operatively coupled with and/or employed byensemble system 102), can comprise such computer and/or machinereadable, writable, and/or executable component(s) and/orinstruction(s). Consequently, according to numerous embodiments,ensemble system 102 and/or any components associated therewith asdisclosed herein, can employ processor 106 to execute such computerand/or machine readable, writable, and/or executable component(s) and/orinstruction(s) to facilitate performance of one or more operationsdescribed herein with reference to ensemble system 102 and/or any suchcomponents associated therewith.

In some embodiments, ensemble system 102 can facilitate performance ofoperations executed by and/or associated with ensemble component 108,score component 110, and/or another component associated with ensemblesystem 102 as disclosed herein. For example, as described in detailbelow, ensemble system 102 can facilitate: generating an ensembleartificial intelligence (AI) model comprising a classical AI model and aquantum AI model; and/or computing probability scores of a dataset basedon the ensemble AI model. In some embodiments, such a classical AI modeland/or a quantum AI model can comprise a boosted AI model comprising twoor more AI models. In some embodiments, ensemble system 102 can furtherfacilitate: computing a quantum kernel and/or one or more quantumsupport vectors; computing a classical kernel and/or one or moreclassical support vectors; computing one or more classical supportvectors based on a classical kernel and/or a quantum kernel; training aclassical AI model based on training data; training a quantum AI modelbased on a subset of training data; generating a boosted classical AImodel comprising two or more classical AI models and/or a boostedquantum AI model comprising two or more quantum AI models; and/orcomputing probability scores of a dataset based on a classical AI modelor a quantum AI model.

In some embodiments, to facilitate performance of such operationsdescribed above, ensemble system 102 and/or one or more componentsthereof can employ one or more kernel methods and/or one or more supportvector machines (SVM) in classical and/or quantum AI models. Forexample, as described in detail below, to facilitate generating anensemble AI model comprising a classical AI model and a quantum AI modeland/or computing probability scores of a dataset based on the ensembleAI model, ensemble system 102 and/or one or more components thereof cancompute a quantum kernel using a quantum computer (e.g., via a quantumkernel library). In this example, ensemble system 102 and/or one or morecomponents thereof can export such a quantum kernel matrix to aclassical system to compute support vectors. In this example, ensemblesystem 102 and/or one or more components thereof can employ a radialbasis function (RBF) kernel to compute a classical kernel and/or one ormore support vectors. In this example, ensemble system 102 and/or one ormore components thereof can employ a boosting technique (e.g., aboosting algorithm) to boost one or more classical AI models and/or oneor more quantum AI models. In this example, ensemble system 102 and/orone or more components thereof can employ a boosting technique (e.g., aboosting algorithm) to generate an ensemble AI model comprising one ormore classical AI models and one or more quantum AI models. In thisexample, ensemble system 102 and/or one or more components thereof cancompute probability scores of the classical and/or quantum AI models. Inthis example, ensemble system 102 and/or one or more components thereofcan employ a quantum computer to compute the dot product between unknownand support vectors corresponding to one or more quantum AI models. Inthis example, ensemble system 102 and/or one or more components thereofcan combine probability scores from classical and/or quantum modelsusing a weighting scheme.

In some embodiments, ensemble system 102 can be implemented to generateand/or execute one or more boosted AI models and/or one or more ensembleAI models to discover effective data representation of classical and/orquantum AI learning models. In some embodiments, ensemble system 102 canbe implemented to generate and/or execute a classical AI model toidentify one or more complex training datasets and/or complexclassification tasks that cannot be executed efficiently and/oreffectively by such a classical AI model (e.g., due to computationalcost). In these embodiments, based on such identification, ensemblesystem 102 can generate and/or execute a quantum AI model to classifysuch complex training dataset(s) and/or perform such complexclassification task(s). In some embodiments, ensemble system 102 can beimplemented to apply a fast-match approach using only one or moreclassical AI models or only one or more quantum AI models to reducesearch space (e.g., to reduce 100 classes to 10 classes, therebyreducing the amount of data (e.g., features) that must be input to aquantum computer). In these embodiments, based on such reduction ofsearch space, ensemble system 102 can apply a detailed-match approach bygenerating and/or implementing an ensemble AI model comprising one ormore classical AI models and/or one or more quantum AI models to make afinal decision using high-dimensional computation techniques of aquantum computing device. In some embodiments, ensemble system 102 canscale to large training datasets by generating and/or implementing oneor more classical AI models to process most of the data and generatingand/or implementing one or more quantum AI models selectively based onsome outcomes or subsampling.

According to multiple embodiments, ensemble component 108 can generatean ensemble AI model comprising one or more classical AI models and oneor more quantum AI models. For example, ensemble component 108 cangenerate an ensemble AI model comprising a classical AI model and aquantum AI model by employing boost component 208 described below withreference to FIG. 2 and/or by employing a boosting technique (e.g., aboosting algorithm such as, for instance, algorithm 300 illustrated inFIG. 3 ). As referenced herein, boosting can comprise a sequentialtechnique which works on the principle of ensemble (e.g., thecombination of one or more individual components to create a singlecomponent). For example, as referenced herein, boosting can comprise asequential technique that can be implemented (e.g., by ensemblecomponent 108) to combine two or more AI models (also referred to aslearners or classifiers) into a single AI model.

In some embodiments, ensemble component 108 can generate an ensemble AImodel comprising a classical AI model and a quantum AI model, where sucha classical AI model and/or quantum AI model can comprise a boosted AImodel that can comprise two or more AI models. For example, ensemblecomponent 108 can generate an ensemble AI model comprising a boostedclassical AI model and a boosted quantum AI model, where such a boostedclassical AI model can comprise two or more classical AI models and sucha boosted quantum AI model can comprise two or more quantum AI models.In another example, ensemble component 108 can generate an ensemble AImodel comprising a boosted classical AI model and a quantum AI model,where such a boosted classical AI model can comprise two or moreclassical AI models. In another example, ensemble component 108 cangenerate an ensemble AI model comprising a classical AI model and aboosted quantum AI model, where such a boosted quantum AI model cancomprise two or more quantum AI models.

In some embodiments, to generate one or more of such ensemble AI modelsdescribed above, ensemble component 108 can implement a boostingtechnique (e.g., a boosting algorithm such as, for instance, algorithm300 illustrated in FIG. 3 ) to combine one or more classical and/orquantum AI models, where such classical AI model(s) can be trained onthe bulk of available training data and/or such quantum AI model(s) canbe trained on a subset of such available training data. For example,ensemble system 102 and/or ensemble component 108 can employ trainercomponent 206 described below with reference to FIG. 2 to train suchclassical AI model(s) on the bulk of available training data and/ortrain such quantum AI model(s) on a subset of such available trainingdata.

According to multiple embodiments, score component 110 can computeprobability scores of a dataset based on an ensemble AI model. Forexample, score component 110 can compute probability scores of a datasetbased on an ensemble AI model that can be generated by ensemblecomponent 108 as described above. In some embodiments, to facilitatesuch computation of probability scores of a dataset based on an ensembleAI model, score component 110 can compute probability scores of thedataset based on a classical AI model and/or a quantum AI model. Forexample, to facilitate such computation of probability scores of adataset based on an ensemble AI model, score component 110 can computeprobability scores of the dataset based on a classical AI model and/or aquantum AI model of such ensemble AI model. In this example, scorecomponent 110 can compute probability scores of the dataset based on aclassical AI model using one or more classical probability scoringtechniques. In this example, score component 110 can compute probabilityscores of the dataset based on a quantum AI model using one or morequantum probability scoring techniques. In these examples, scorecomponent 110 can combine such probability scores based on generation ofthe ensemble AI model (e.g., via ensemble component 108), therebyfacilitating computation of probability scores of a dataset based on anensemble AI model. For instance, score component 110 can computeprobability scores of a dataset based on a classical AI model, a quantumAI model, and/or an ensemble AI model which can be presented in the formof a table such as, for example, table 800 a depicted in FIG. 8A and/orin the form of a matrix such as, for example, matrix 800 b and/or matrix800 c depicted in FIGS. 8B and 8C, respectively.

FIG. 2 illustrates a block diagram of an example, non-limiting system200 that can facilitate a classical and quantum ensemble artificialintelligence (AI) model in accordance with one or more embodimentsdescribed herein. Repetitive description of like elements and/orprocesses employed in respective embodiments is omitted for sake ofbrevity. In some embodiments, system 200 can comprise ensemble system102. In some embodiments, ensemble system 102 can comprise a quantumcomputing component 202, a classical computing component 204, a trainercomponent 206, and/or a boost component 208.

According to multiple embodiments, quantum computing component 202 cancomprise a quantum computing device including, but not limited to, aquantum computer, a quantum processor, a quantum circuit, asuperconducting circuit, a simulated quantum computer (e.g., softwareexecuted on a classical computer that simulates one or more operationsof a quantum computer), and/or another quantum computing device. In someembodiments, quantum computing component 202 can compute a quantumkernel and/or one or more quantum support vectors. In some embodiments,as described above with reference to FIG. 1 , ensemble system 102 and/orone or more components thereof can employ one or more kernel methodsand/or one or more support vector machines (SVM) in classical and/orquantum AI models. For example, to facilitate generating an ensemble AImodel comprising a classical AI model and a quantum AI model and/orcomputing probability scores of a dataset based on the ensemble AImodel, quantum computing component 202 can compute a quantum kernel(e.g., a quantum kernel matrix) using a quantum kernel library and canfurther compute one or more quantum support vectors.

As referenced herein, a kernel method can map data of a dataset intohigher dimensional spaces to facilitate improved separation (e.g.,classification) of such data. In some embodiments, based on a pair ofdata points x and z, a kernel function k can be defined ask(x,z)=ϕ(x)^(T)ϕ(z), where ϕ can be a feature map function, and T can bea transpose of a vector. In these embodiments, there are no constraintson the form of this mapping ϕ(x) could be infinite. In some embodiments,quantum computing component 202 can compute the dot product betweenunknown and support vectors corresponding to one or more quantum AImodels. In some embodiments, quantum computing component 202 can computeinner products that can provide a measure of similarity. In someembodiments, such inner product in a two-dimensional (2D) space between2 vectors of unit length can return the cosine of the angle between suchvectors, which can indicate how far apart they are. For instance, ifthey are parallel, their inner product is 1 (e.g., completely similar).Conversely, in another example, if they are perpendicular (e.g.,completely dissimilar) their inner product is 0, and thus, should notcontribute to the correct AI model (e.g. classifier, learner).

In some embodiments, ensemble system 102 (e.g., quantum computingcomponent 202, classical computing component 204, etc.) can implement akernel trick that can provide a bridge from linearity to non-linearityto any algorithm. In some embodiments, such a kernel trick can beexpressed solely in terms of dot products between two vectors. Forexample, ensemble system 102 (e.g., quantum computing component 202,classical computing component 204, etc.) can implement one or more shiftinvariant kernels such as, for instance, Gaussian radial basis function(RBF) and/or a Laplacian, as defined by equations (1) and (2) below. Insome embodiments, ensemble system 102 (e.g., quantum computing component202, classical computing component 204, etc.) can map input data into ahigher-dimensional space, where a linear algorithm operating in such ahigher-dimensional space can behave non-linearly in the original inputspace.k ^(rbf)=exp(^(−∥x−z∥2)/2ρ²)  (1)k ^(lap)=exp(^(−∥x−z∥)/σ)  (2)

where:

k^(rbf) and k^(lap) can be Radial Basis Function and Laplacian kernels,respectively;

∥x−z∥ denotes the Euclidean distance between two feature vectors; and

σ denotes a tunable free parameter.

In some embodiments, ensemble system 102 (e.g., quantum computingcomponent 202, classical computing component 204, etc.) can implementone or more kernel machines such as, for example, support vectormachines (SVM) comprising support vectors (e.g., as illustrated in FIG.6A), where such support vector machines can approximate any functionbased on a large quantity of training data. In some embodiments,ensemble system 102 (e.g., quantum computing component 202, classicalcomputing component 204, etc.) can overcome computational complexity ofkernel methods applied to a large-scale problem, where data of alarge-scale problem cannot be separated by a linear function. Forexample, ensemble system 102 (e.g., quantum computing component 202,classical computing component 204, etc.) can overcome computationalcomplexity of kernel methods applied to a large-scale problem byformulating such a problem as a quadratic programming problem (e.g.,mapping a function such as, for instance, a linear function to quadraticas illustrated in FIG. 6B). In these embodiments, such a quadraticprogramming problem can comprise a time complexity of O(m³) and a spacecomplexity of O(m²), where m can denote the number of training samples.

In some embodiments, ensemble system 102 (e.g., quantum computingcomponent 202, classical computing component 204, etc.) can implement asupport vector machine as a constrained optimization problem, forexample, to maximize the margin illustrated in FIG. 6A. For example,ensemble system 102 (e.g., quantum computing component 202, classicalcomputing component 204, etc.) can implement a support vector machine asa constrained optimization problem that can yield a dual quadraticprogram that only uses access to the kernel K({right arrow over(x)}_(i),{right arrow over (x)}_(j)) for {right arrow over (x)}_(i) intraining set T, where such a constrained optimization problem can bedefined by equation (3) below:

$\begin{matrix}{{L_{D}(\alpha)} = {{\sum\limits_{i \in T}^{\;}\alpha_{i}} - {\frac{1}{2}{\sum\limits_{i,{j \in T}}^{\;}{k_{i}k_{j}\alpha_{i}\alpha_{j}{K\left( {{\overset{->}{x}}_{i},{\overset{->}{x}}_{j}} \right)}}}}}} & (3)\end{matrix}$

where:

α_(i) denotes the weight corresponding to a support vector (e.g., wheremost of the weights are zero); and

k_(i) denotes the corresponding label of a training sample i.

In some embodiments, α_(i)*>0 can correspond to support vectors and thedecision function can be defined by equation (4) below:{tilde over (m)}({right arrow over (s)})=sign(Σ_(i∈N) _(S) α_(i) k _(i)K({right arrow over (x)}_(i) ,{right arrow over (s)})+b)  (4)

where:

N denotes the number of support vectors;

α_(i) denotes the support vector weight;

k_(i) denotes the label corresponding to the support vector;

K denotes the kernel between unknown and support vector; and

b denotes the bias term.

In some embodiments, ensemble system 102 (e.g., quantum computingcomponent 202, classical computing component 204, etc.) can implementquantum enhanced feature spaces, where quantum support vector machinescan offer advantages over conventional (e.g., classical) support vectormachines if the quantum feature map leads to a kernel that cannot beefficiently calculated classically (e.g., via a classical computer). Forexample, ensemble system 102 (e.g., quantum computing component 202,classical computing component 204, etc.) can implement one or morequantum support vector machines based on equations (5) and (6) belowand/or quantum feature map 600 c depicted in FIG. 6C.{right arrow over (x)}

|Φ({right arrow over (x)})

=

_(101 ({right arrow over (x)}))|0

^(n)  (5)

where |Φ({right arrow over (x)})

=

_(101 ({right arrow over (x)}))|0

^(n) denotes the feature map on n qubits.K({right arrow over (x)},{right arrow over (y)})=|

Φ({right arrow over (x)})|Φ({right arrow over (y)})

|²  (6)

where K(x,y) denotes the quantum Kernel.

According to multiple embodiments, classical computing component 204 cancomprise any type of classical computing component, machine, device,facility, apparatus, and/or instrument that comprises a processor and/orcan be capable of effective and/or operative communication with a wiredand/or wireless network. All such embodiments are envisioned. Forexample, classical computing component 204 can comprise a server device,a classical computer, a classical general-purpose computer, a classicalspecial-purpose computer, a tablet computing device, a handheld device,a server class computing machine and/or database, a laptop computer, anotebook computer, a desktop computer, a cell phone, a smart phone, aconsumer appliance and/or instrumentation, an industrial and/orcommercial device, a digital assistant, a multimedia Internet enabledphone, a multimedia players, and/or another type of classical computingcomponent, machine, device, facility, apparatus, and/or instrument.

In some embodiments, classical computing component 204 can compute aclassical kernel and/or one or more classical support vectors. Forexample, classical computing component 204 can compute a classicalkernel by employing a radial basis function (RBF) kernel. In someembodiments, classical computing component 204 can compute one or moreclassical support vectors based on the classical kernel or a quantumkernel (e.g., a quantum kernel and/or quantum kernel matrix that can becomputed by quantum computing component 202 as described above).

According to multiple embodiments, trainer component 206 can train aclassical AI model based on training data and/or train a quantum AImodel based on a subset of the training data. For example, trainercomponent 206 can train a classical AI model based on all data of atraining dataset, where such a classical AI model can be implemented by,for instance, classical computing component 204. In this example,trainer component 206 can further train a quantum AI model based on asubset of such a training dataset, where such a quantum AI model can beimplemented by, for instance, quantum computing component 202.

In some embodiments, trainer component 206 can train a classical AImodel based on training data and/or a quantum AI model based on a subsetof such training data by employing one or more learning algorithmsincluding, but not limited to, a supervised learning algorithm, asemi-supervised learning algorithm, an unsupervised learning algorithm,a reinforcement learning algorithm, and/or another learning algorithm.In some embodiments, trainer component 206 can train a classical AImodel based on training data and/or a quantum AI model based on a subsetof such training data by employing script 700 c illustrated in FIG. 7C.

In some embodiments, ensemble system 102 (e.g., via classical computingcomponent 204) can implement one or more classical AI models to identifyone or more complex training datasets (e.g., subsets of the originaltraining data) and/or one or more complex classification tasks thatcannot be efficiently and/or effectively processed (e.g., from acomputational standpoint) by a classical computing device (e.g., byclassical computing component 204) using such classical AI model(s). Inthese embodiments, ensemble system 102 can employ a quantum computingdevice (e.g., quantum computing component 202) to implement one or morequantum AI models that can classify such complex training dataset(s)and/or execute such complex classification tasks. In these embodiments,trainer component 206 can train such quantum AI models based on suchcomplex training dataset(s) that can comprise subset(s) of the originaltraining data.

According to multiple embodiments, boost component 208 can generate aboosted classical AI model comprising two or more classical artificialintelligence models and/or a boosted quantum AI model comprising two ormore quantum artificial intelligence models. In some embodiments, togenerate such a boosted classical AI model and/or a boosted quantum AImodel, boost component 208 can employ a boosting algorithm (e.g., anadaptive boosting algorithm) to combine one or more classical AI modelsand/or to combine one or more quantum AI models. For example, togenerate such a boosted classical AI model and/or a boosted quantum AImodel, boost component 208 can employ algorithm 300 described below andillustrated in FIG. 3 to combine one or more classical AI models and/orto combine one or more quantum AI models (e.g., as described below andillustrated in FIGS. 4 and 5 ).

FIG. 3 illustrates an example, non-limiting algorithm 300 that canfacilitate a classical and quantum ensemble artificial intelligence (AI)model in accordance with one or more embodiments described herein.Repetitive description of like elements and/or processes employed inrespective embodiments is omitted for sake of brevity.

According to multiple embodiments, algorithm 300 can comprise a boostingalgorithm (e.g., an adaptive boosting algorithm). In some embodiments,ensemble system 102 and/or components thereof (e.g., ensemble component108, score component 110, boost component 208, etc.) can facilitateperformance of various operations described herein by executing one ormore sections of algorithm 300. For example, as described above withreference to FIGS. 1 and 2 , ensemble system 102 and/or componentsthereof (e.g., ensemble component 108, score component 110, boostcomponent 208, etc.) can employ algorithm 300 to boost one or more AImodels (e.g., classical and/or quantum AI models) and/or to generate anensemble AI model comprising one or more classical AI models and/or oneor more quantum AI models. In some embodiments, algorithm 300 cancomprise an adaptive boosting algorithm that can change sampledistribution by modifying one or more weights corresponding to trainingdata. For example, as described below with reference to FIG. 5 ,algorithm 300 can comprise an adaptive boosting algorithm that, whenimplemented (e.g., by ensemble component 108, score component 110,etc.), can change sample distribution by modifying one or more weightscorresponding to training data.

FIG. 4 illustrates an example, non-limiting system 400 that canfacilitate a classical and quantum ensemble artificial intelligence (AI)model in accordance with one or more embodiments described herein.Repetitive description of like elements and/or processes employed inrespective embodiments is omitted for sake of brevity.

In some embodiments, system 400 can comprise one or more AI models 402a, 402 b, 402 n (where n can represent a total quantity of AI models),one or more AI model results 404 a, 404 b, 404 n (where n can representa total quantity of AI models), a boosted AI model 406, and/or a boostedAI model results 408. In some embodiments, AI models 402 a, 402 b, 402 ncan comprise one or more classical AI models and/or one or more quantumAI models. In some embodiments, AI model results 404 a, 404 b, 404 n cancomprise classifier results of AI models 402 a, 402 b, 402 n that can beimplemented to classify (e.g., label, categorize, etc.) one or moreentities of a dataset, where such entities are represented by plussymbols (+) and minus symbols (−) in FIG. 4 . In some embodiments, asillustrated in FIG. 4 , AI model results 404 a, 404 b, 404 n cancomprise one or more decision boundaries 410 a, 410 b, 410 n (where ncan represent a total quantity of decision boundaries). In someembodiments, boosted AI model 406 and/or boosted AI model results 408can comprise a weighted combination of one or more AI models 402 a, 402b, 402 n and/or one or more AI model results 404 a, 404 b, 404 n.

In some embodiments, as described above with reference to FIG. 1 , togenerate an ensemble AI model comprising one or more classical AI modelsand/or one or more quantum AI models, ensemble component 108 canimplement a boosting technique (e.g., a boosting algorithm such as, forinstance, algorithm 300 illustrated in FIG. 3 ) to combine two or moreAI models and/or to iteratively add one or more AI models to an existingensemble AI model. In these embodiments, such combination and/oriterative addition can be represented by AI models 402 a, 402 b, 402 n,AI model results 404 a, 404 b, 404 n, boosted AI model 406, and/orboosted AI model results 408 illustrated in FIG. 4 . For example, ateach stage, ensemble component 108 can introduce (e.g., add) an AI model(e.g., a weak performing learner or classifier) to compensate the“shortcomings” of one or more AI models of an ensemble AI model (e.g.,one or more weak performing learners or classifiers of a previouslygenerated ensemble AI model) by high-weight data points.

In some embodiments, at instant t, ensemble component 108 can weighoutcomes of an ensemble AI model (e.g., outcomes of each individual AImodel of such an ensemble AI model) based on the outcomes of a previousinstance, at t−1, for example. In some embodiments, for example, asillustrated by system 500 described below and depicted in FIG. 5 ,ensemble component 108 can assign a lower weight value to correctlyclassified outcomes and/or a higher weight value to miss-classifiedoutcomes.

In some embodiments, as described above with reference to FIG. 2 , togenerate a boosted classical AI model comprising two or more classicalAI models and/or a boosted quantum AI model comprising two or morequantum AI models, boost component 208 can implement a boostingtechnique (e.g., a boosting algorithm such as, for instance, algorithm300 illustrated in FIG. 3 ) to combine two or more AI models and/or toiteratively add one or more AI models to an existing boosted AI model.In these embodiments, such combination and/or iterative addition can berepresented by AI models 402 a, 402 b, 402 n, AI model results 404 a,404 b, 404 n, boosted AI model 406, and/or boosted AI model results 408illustrated in FIG. 4 . For example, at each stage, boost component 208can introduce (e.g., add) an AI model (e.g., a weak performing learneror classifier) to compensate the “shortcomings” of one or more AI modelsof a boosted AI model (e.g., one or more weak performing learners orclassifiers of a previously generated boosted AI model) by high-weightdata points.

In some embodiments, at instant t, boost component 208 can weighoutcomes of a boosted AI model (e.g., outcomes of each individual AImodel of such a boosted AI model) based on the outcomes of a previousinstance, at t−1, for example. In some embodiments, for example, asillustrated by system 500 described below and depicted in FIG. 5 , boostcomponent 208 can assign a lower weight value to correctly classifiedoutcomes and/or a higher weight value to miss-classified outcomes.

FIG. 5 illustrates an example, non-limiting system 500 that canfacilitate a classical and quantum ensemble artificial intelligence (AI)model in accordance with one or more embodiments described herein.Repetitive description of like elements and/or processes employed inrespective embodiments is omitted for sake of brevity.

In some embodiments, as described above with reference to FIG. 1 ,ensemble component 108 can employ algorithm 300 illustrated in FIG. 3 toboost one or more AI models and/or to generate an ensemble AI modelcomprising one or more classical AI models and/or one or more quantum AImodels. In some embodiments, algorithm 300 can comprise an adaptiveboosting algorithm that can change sample distribution by modifying oneor more weights corresponding to training data. For example, algorithm300 can comprise an adaptive boosting algorithm that, when implemented(e.g., by ensemble component 108, score component 110, etc.), can changesample distribution by modifying one or more weights 502 a, 502 b, 502 n(where n can represent a total quantity of weights) corresponding totraining data represented by plus symbols (+) and minus symbols (−) inFIGS. 4 and 5 . In some embodiments, ensemble component 108 can employalgorithm 300 to increase the weight of mis-classified data and decreasethe weight of correctly classified data (e.g., as illustrated in FIGS. 4and 5 ). In some embodiments, based on training one or more AI models(e.g., via trainer component 206) ensemble component 108 can add theweight of a weak performing AI model (e.g., a weak learner orclassifier) to an ensemble AI model based on the performance of such aweak performing AI model. In some embodiments, the better a weakperforming AI model performs, the more it contributes to the ensemble AImodel.

In some embodiments, ensemble component 108 can facilitate such increaseand/or decrease in weights corresponding to training data as describedabove based on an output of algorithm 300, which can comprise equation(7) below:H(x)=sign(Σ_(t=1) ^(T)α_(t) h _(t)(x))  (7)

where:

T denotes the number of component classifiers;

α_(t) denotes the weight of the component classifier; and

h_(t) denotes the component classifier model (e.g., SVM classifiers,using classical RBF and Quantum kernels).

In some embodiments, in training a boosted AI model and/or an ensembleAI model, a weak performing AI model (e.g., learner, classifier, etc.)may use the weights or data can be subsampled according to thedistribution of weights. In some embodiments, the weight of a componentclassifier can be≥0 if error≤½, the smaller the error the higher theweight.

FIG. 6A illustrates an example, non-limiting system 600 a that canfacilitate a classical and quantum ensemble artificial intelligence (AI)model in accordance with one or more embodiments described herein.Repetitive description of like elements and/or processes employed inrespective embodiments is omitted for sake of brevity.

In some embodiments, FIG. 6A can comprise a visual representation of howan AI model can classify a dataset into two or more data classes. Forexample, in some embodiments, system 600 a can comprise an AI model suchas, for instance, a support vector machine (SVM) that, when implementedby ensemble system 102 (e.g., via quantum computing component 202,classical computing component 204, etc.), can classify a dataset intotwo or more data classes 602 a, 602 b, where data class 602 a isdepicted in FIG. 6A as gray dots and data class 602 b is depicted asblack dots. In some embodiments, for example, in embodiments wheresystem 600 a comprises a SVM, system 600 a can determine (e.g., compute,identify, etc.) support vectors 604 a, 604 b that can maximize a margin606 that can separate data class 602 a and data class 602 b, wheremargin 606 can comprise a distance between data class 602 a and dataclass 602 b.

FIG. 6B illustrates an example, non-limiting system 600 b that canfacilitate a classical and quantum ensemble artificial intelligence (AI)model in accordance with one or more embodiments described herein.Repetitive description of like elements and/or processes employed inrespective embodiments is omitted for sake of brevity.

In some embodiments, FIG. 6B can comprise a visual representation of howa dataset 608 in a low-dimensional space 610 (e.g., a one-dimensionalspace, a linear space, etc.) can be mapped to a high-dimensional space612 (e.g., a multi-dimensional space, a quadratic space, etc.) and/orhow an AI model can classify dataset 608 into two or more data classes602 a, 602 b in such a high-dimensional space 612. For example, in someembodiments, system 600 b can comprise an AI model such as, forinstance, a support vector machine (SVM). In this example, FIG. 6B cancomprise a visual representation of how ensemble system 102 (e.g., viaquantum computing component 202, classical computing component 204,etc.) can implement a kernel trick (e.g., as described above withreference to FIG. 2 ) to formulate such an SVM as a quadraticprogramming problem (e.g., a quantum SVM) by mapping dataset 608 fromlow-dimensional space 610 to high-dimensional space 612 and classifyingdataset 608 into data classes 602 a, 602 b in high-dimensional space612. In some embodiments, to facilitate such a kernel trick formulationof an SVM as a quadratic programming problem (e.g., a quantum SVM)and/or to facilitate such classification of dataset 608 into dataclasses 602 a, 602 b, ensemble system 102 (e.g., via quantum computingcomponent 202, classical computing component 204, etc.) can construct ahyperplane w defined by equation (8) below:w·{right arrow over (x)}+b=0  (8)

where:

w denotes a vector;

x denotes a set of data points; and

b denotes a bias. As referenced herein, a hyperplane (e.g., anyhyperplane) can be written as the set of points x satisfying w·x+b=0.

FIG. 6C illustrates an example, non-limiting quantum feature map 600 cthat can facilitate a classical and quantum ensemble artificialintelligence (AI) model in accordance with one or more embodimentsdescribed herein. Repetitive description of like elements and/orprocesses employed in respective embodiments is omitted for sake ofbrevity.

In some embodiments, quantum feature map 600 c can comprise a two-layermap that can comprise Hadamard and entanglement gates, where quantumfeature map 600 c cannot be implemented classically (e.g., via aclassical computer). In some embodiments, data of quantum feature map600 c can be between zero and 2PI. In some embodiments, quantum featuremap 600 c can encode both the actual function of the diagonal phases aswell as the corresponding Fourier-Walsh transform. In some embodiments,ensemble system 102 (e.g., via quantum computing component 202,classical computing component 204, etc.) can employ quantum feature map600 c and/or equations (3), (4), (5), and (6) defined above withreference to FIG. 2 , to facilitate such a kernel trick formulation ofan SVM as a quadratic programming problem (e.g., a quantum SVM) and/orto facilitate such classification of dataset 608 into data classes 602a, 602 b as described above and illustrated in FIG. 6B.

FIGS. 7A, 7B, 7C, and 7D illustrate example, non-limiting scripts 700 a,700 b, 700 c, 700 d that can facilitate a classical and quantum ensembleartificial intelligence (AI) model in accordance with one or moreembodiments described herein. Repetitive description of like elementsand/or processes employed in respective embodiments is omitted for sakeof brevity.

In some embodiments, ensemble system 102 (e.g., via quantum computingcomponent 202, classical computing component 204, etc.) can executescript 700 a (FIG. 7A) to compute the quantum kernel described abovewith reference to FIG. 1 . For example, quantum computing component 202can execute script 700 a to compute a quantum kernel inqsvm_kernel_bynary.py.

In some embodiments, ensemble system 102 (e.g., via quantum computingcomponent 202, classical computing component 204, etc.) can executescript 700 b (FIG. 7B) to implement the kernel trick described abovewith reference to FIGS. 2, 6B, and 6C, where such a kernel trick canprovide a bridge from linearity to non-linearity to any algorithm. Forexample, ensemble system 102 (e.g., via quantum computing component 202,classical computing component 204, etc.) can execute script 700 b togenerate a custom kernel that can provide a bridge from linearity tonon-linearity to any algorithm. For instance, as described above withreference to FIG. 6B, ensemble system 102 (e.g., via quantum computingcomponent 202, classical computing component 204, etc.) can executescript 700 b to generate a custom kernel (e.g., an SVM formulated as aquadratic programming problem) that can facilitate mapping a dataset(e.g., dataset 608) from a low-dimensional space (e.g., low-dimensionalspace 610) to a high-dimensional space (e.g., high-dimensional space612) and classifying such a dataset into data classes (e.g., dataclasses 602 a, 602 b) in such a high-dimensional space.

In some embodiments, ensemble system 102 (e.g., via ensemble component108, score component 110, quantum computing component 202, classicalcomputing component 204, trainer component 206, boost component 208,etc.) can execute script 700 c (FIG. 7C) to define one or more AImodels. For example, ensemble system 102 (e.g., via ensemble component108, score component 110, quantum computing component 202, classicalcomputing component 204, trainer component 206, boost component 208,etc.) can execute script 700 c to define one or more AI modelsincluding, but not limited to, one or more classical AI models, one ormore quantum AI models, one or more boosted classical AI models, one ormore boosted quantum AI models, one or more ensemble AI models (e.g.,comprising at least one classical AI model and at least one quantum AImodel), and/or another AI model. For instance, ensemble component 108and/or boost component 208 can execute script 700 c to define anensemble AI model as described above with reference to FIGS. 1, 3, 4,and 5 and/or a boosted AI model (e.g., a boosted classical AI modeland/or a boosted quantum AI model) as described above with reference toFIGS. 2, 3, 4, and 5 .

In some embodiments, ensemble system 102 (e.g., via ensemble component108, score component 110, quantum computing component 202, classicalcomputing component 204, trainer component 206, boost component 208,etc.) can execute script 700 c (FIG. 7C) to train one or more AI models.For example, ensemble system 102 (e.g., via ensemble component 108,score component 110, quantum computing component 202, classicalcomputing component 204, trainer component 206, boost component 208,etc.) can execute script 700 c to train one or more AI models including,but not limited to, one or more classical AI models, one or more quantumAI models, one or more boosted classical AI models, one or more boostedquantum AI models, one or more ensemble AI models (e.g., comprising atleast one classical AI model and at least one quantum AI model), and/oranother AI model. For instance, trainer component 206 can execute script700 c to train a classical AI model (e.g., of a boosted classical AImodel and/or of an ensemble AI model) based on all data of a trainingdataset and/or to train a quantum AI model (e.g., of a boosted quantumAI model and/or of an ensemble AI model) based on a subset of suchtraining dataset as described above with reference to FIG. 2 .

In some embodiments, ensemble system 102 (e.g., via score component 110,quantum computing component 202, classical computing component 204,etc.) can execute script 700 c (FIG. 7C) to test one or more AI models.For example, ensemble system 102 (e.g., via score component 110, quantumcomputing component 202, classical computing component 204, etc.) canexecute script 700 c to test one or more AI models including, but notlimited to, one or more classical AI models, one or more quantum AImodels, one or more boosted classical AI models, one or more boostedquantum AI models, one or more ensemble AI models (e.g., comprising atleast one classical AI model and at least one quantum AI model), and/oranother AI model. For instance, ensemble system 102 (e.g., via scorecomponent 110, quantum computing component 202, classical computingcomponent 204, etc.) can execute script 700 c to test a boosted AI model(e.g., a boosted classical AI model, a boosted quantum AI model, etc.)generated by boost component 208 as described above with reference toFIGS. 2, 3, 4, and 5 and/or to test an ensemble AI model generated byensemble component 108 as described above with reference to FIGS. 1, 3,4, and 5 .

In some embodiments, ensemble system 102 (e.g., via ensemble component108, score component 110, quantum computing component 202, classicalcomputing component 204, boost component 208, etc.) can execute script700 d (FIG. 7D) to generate one or more boosted AI models (e.g., boostedclassical AI model, boosted quantum AI model, etc.) and/or one or moreensemble AI models (e.g., comprising at least one classical AI model andat least one quantum AI model). For example, ensemble component 108 canexecute script 700 d to generate one or more ensemble AI models asdescribed above with reference to FIGS. 1, 3, 4, and 5 . In anotherexample, boost component 208 can execute script 700 d to generate one ormore boosted AI models as described above with reference to FIGS. 2, 3,4, and 5 .

In some embodiments, ensemble system 102 (e.g., via ensemble component108, score component 110, quantum computing component 202, classicalcomputing component 204, boost component 208, etc.) can execute script700 d (FIG. 7D) to compute probability scores of a dataset based on anensemble AI model. For example, score component 110 can execute script700 d to compute probability scores of a dataset based on an ensemble AImodel that can be generated by ensemble component 108 as described abovewith reference to FIGS. 1, 3, 4, and 5 .

FIG. 8A illustrates an example, non-limiting table 800 a that canfacilitate a classical and quantum ensemble artificial intelligence (AI)model in accordance with one or more embodiments described herein.Repetitive description of like elements and/or processes employed inrespective embodiments is omitted for sake of brevity.

According to multiple embodiments, table 800 a can comprise one or moreprobability scores 802 (e.g., denoted as percentage (%) values in FIG.8A) corresponding to one or more datasets 804 (e.g., denoted as task(train×test) in FIG. 8A) based on one or more AI models 806 that can beimplemented by ensemble system 102. For example, table 800 a cancomprise one or more probability scores 802 that can be computed byscore component 110 as described above with reference to FIG. 1 , wheresuch probability scores 802 can correspond to one or more datasets 804(e.g., Ad-hoc (96×24), Iris (119×30), Digits (280×70) 3Qubits, etc.)based on one or more AI models 806. In some embodiments, table 800 a cancomprise quantum kernel compute time 808 expressed in minutes (e.g.,denoted as Q-Kernel compute in min in FIG. 8A), where quantum kernelcompute time 808 can comprise the time it takes an AI model 806 (e.g.,an AI model generated based on a quantum kernel) to classify a dataset804.

In some embodiments, score component 110 can compute probability scores802 corresponding to datasets 804 based on one or more AI models 806generated by and/or implemented by ensemble system 102. For example,score component 110 can compute probability scores 802 corresponding todatasets 804 based on one or more AI models 806 generated by and/orimplemented by ensemble system 102 (e.g., via ensemble component 108,boost component 208, etc.), where such one or more AI models 806 caninclude, but are not limited to: a quantum support vector machine(QSVM); a classical support vector machine (SVM); a boosted classicalsupport vector machine (Boosted SVM); an ensemble AI model (SVM+QSVM)comprising a classical support vector machine and a quantum supportvector machine; an ensemble AI model (Boosted SVM+QSVM) comprising aboosted classical support vector machine and a quantum support vectormachine; a boosted quantum support vector machine (Boosted QSVM); anensemble AI model (Boosted QSVM+Boosted SVM) comprising a boostedquantum support vector machine and a boosted classical support vectormachine. In this example, ensemble system 102 and/or score component 110can generate table 800 a based on computation of probability scores 802by score component 110.

FIGS. 8B and 8C illustrate example, non-limiting matrices 800 b, 800 cthat can facilitate a classical and quantum ensemble artificialintelligence (AI) model in accordance with one or more embodimentsdescribed herein. Repetitive description of like elements and/orprocesses employed in respective embodiments is omitted for sake ofbrevity.

According to multiple embodiments, matrix 800 b (FIG. 8B) can comprise anormalized confusion matrix. In some embodiments, score component 110can compute probability scores 802 (e.g., denoted as decimal numbers inFIG. 8B) corresponding to a dataset 804 (e.g., the 3^(rd) Party (320×80)3Qubits dataset illustrated in FIG. 8A) based on one or more AI models806 generated by and/or implemented by ensemble system 102 (e.g., the AImodels defined above with reference to FIG. 8A).

According to multiple embodiments, matrix 800 c (FIG. 8C) can comprise anormalized confusion matrix. In some embodiments, score component 110can compute probability scores 802 (e.g., denoted as decimal numbers inFIG. 8B) corresponding to a dataset 804 (e.g., the Digits (280×70)3Qubits dataset illustrated in FIG. 8A) based on one or more AI models806 generated by and/or implemented by ensemble system 102 (e.g., the AImodels defined above with reference to FIG. 8A). For example, scorecomponent 110 can compute probability scores 802 of matrix 800 c thatcorrespond to a dataset 804 comprising numerical digits zero (0), one(1), two (2), three (3), four (4), five (5), six (6), seven (7), eight(8), and nine (9) as illustrated in FIG. 8C, where score component 110can compute such probability scores 802 based on one or more AI models806 generated by and/or implemented by ensemble system 102 (e.g., the AImodels defined above with reference to FIG. 8A).

In some embodiments, as described above with reference to FIG. 2 ,ensemble system 102 (e.g., via classical computing component 204) canimplement one or more classical AI models to identify one or morecomplex training datasets (e.g., subsets of the original training data)and/or one or more complex classification tasks that cannot beefficiently and/or effectively processed (e.g., from a computationalstandpoint) by a classical computing device (e.g., by classicalcomputing component 204) using such classical AI model(s). For example,based on score component 110 computing a probability score of 0.00corresponding to classification of digit number six (6) as depicted inFIG. 8C, ensemble system 102 can identify the dataset of matrix 800 cand/or data corresponding to digit number six (6) as complex trainingdata and/or as a complex classification task. In this example, based onsuch identification, ensemble system 102 can employ a quantum computingdevice (e.g., quantum computing component 202) to generate and/orimplement one or more quantum AI models that can effectively classifythe digit number six (6) based only on training data corresponding thedigit number six (6), which can comprise a subset of the originaltraining data of the dataset of matrix 800 c.

FIG. 8D illustrates an example, non-limiting plot 800 d that canfacilitate a classical and quantum ensemble artificial intelligence (AI)model in accordance with one or more embodiments described herein.Repetitive description of like elements and/or processes employed inrespective embodiments is omitted for sake of brevity.

According to multiple embodiments, plot 800 d can comprise a visualrepresentation of data entities of a principle component analysis (e.g.,denoted as PCA in FIG. 8D), where the X-axis of plot 800 d can compriseFeature 1 and the Y-axis can comprise Feature 2. For example, plot 800 dcan comprise a PCA reduced features of Digits dataset to 2 dimensions,where plot 800 d can depict distributed data entities of such reducedDigits dataset. For instance, plot 800 d can comprise a visualrepresentation of data entities of a reduced Digits dataset such as, forinstance, the training data corresponding to the digit number six (6) ofmatrix 800 c that can be identified by ensemble system 102 as complextraining data and/or as a complex classification task as described abovewith reference to FIG. 8C. In this example, ensemble system 102 cangenerate plot 800 d comprising only such training data corresponding tothe digit number six (6) of matrix 800 c and can further generate and/orimplement a quantum AI model (e.g., a single quantum AI model, a boostedquantum AI model, etc.) to effectively classify the digit number six (6)of the dataset of matrix 800 c.

In some embodiments, ensemble system 102 can be associated with varioustechnologies. For example, ensemble system 102 can be associated withclassical computing technologies, quantum computing technologies,classical AI model technologies, quantum AI model technologies,classical AI model boosting technologies, quantum AI model boostingtechnologies, ensemble AI model technologies, optimization technologies,quantum computer programming technologies, and/or other technologies.

In some embodiments, ensemble system 102 can provide technicalimprovements to systems, devices, components, operational steps, and/orprocessing steps associated with the various technologies identifiedabove. For example, ensemble system 102 can facilitate improved datarepresentations by combining classical AI models and/or quantum AImodels. In another example, ensemble system 102 can generate and/orexecute one or more boosted AI models and/or one or more ensemble AImodels to discover effective data representation of classical and/orquantum AI learning models. In another example, ensemble system 102 cangenerate and/or execute a classical AI model to identify one or morecomplex training datasets and/or complex classification tasks thatcannot be executed efficiently and/or effectively by such a classical AImodel (e.g., due to computational cost). In this example, based on suchidentification, ensemble system 102 can generate and/or execute aquantum AI model to classify such complex training dataset(s) and/orperform such complex classification task(s). In another example,ensemble system 102 can apply a fast-match approach using only one ormore classical AI models or only one or more quantum AI models to reducesearch space (e.g., to reduce 100 classes to 10 classes, therebyreducing the amount of data (e.g., features) that must be input to aquantum computer). In this example, based on such reduction of searchspace, ensemble system 102 can apply a detailed-match approach bygenerating and/or implementing an ensemble AI model comprising one ormore classical AI models and/or one or more quantum AI models to make afinal decision using high-dimensional computation techniques of aquantum computing device. In another example, ensemble system 102 canscale to large training datasets by generating and/or implementing oneor more classical AI models to process most of the data and generatingand/or implementing one or more quantum AI models selectively based onsome outcomes or subsampling.

In some embodiments, ensemble system 102 can provide technicalimprovements to a processing unit (e.g., processor 106) associated witha classical computing device (e.g., classical computing component 204)and/or a quantum computing device (e.g., quantum computing component202, a quantum computer, a quantum processor, quantum hardware, etc.).For example, by implementing one or more classical AI models based onall data of a training dataset, implementing one or more quantum AImodels based on a subset of the training dataset, and implementing anensemble AI model comprising one or more classical AI models and one ormore quantum AI models (e.g., where such an ensemble AI model can begenerated based on a quantum kernel matrix), ensemble system 102 canreduce processing time and/or processing workload of such a processingunit (e.g., processor 106), thereby facilitating improved processingperformance of such a processing unit. In this example, based onimplementing such an ensemble AI model, ensemble system 102 can furtherfacilitate improved probability scores of the training dataset.

In some embodiments, ensemble system 102 can employ hardware or softwareto solve problems that are highly technical in nature, that are notabstract and that cannot be performed as a set of mental acts by ahuman. In some embodiments, some of the processes described herein canbe performed by one or more specialized computers (e.g., specializedclassical computer(s), specialized classical processing unit(s),specialized quantum computer(s), specialized quantum processing unit(s),etc.) for carrying out defined tasks related to the various technologiesidentified above. In some embodiments, ensemble system 102 or componentsthereof, can be employed to solve new problems that arise throughadvancements in technologies mentioned above, employment of quantumcomputing systems, cloud computing systems, computer architecture,and/or another technology.

It is to be appreciated that ensemble system 102 can utilize variouscombinations of electrical components, mechanical components, andcircuitry that cannot be replicated in the mind of a human or performedby a human, as the various operations that can be executed by ensemblesystem 102 or components thereof as described herein are operations thatare greater than the capability of a human mind. For instance, theamount of data processed, the speed of processing such data, or thetypes of data processed by ensemble system 102 over a certain period oftime can be greater, faster, or different than the amount, speed, ordata type that can be processed by a human mind over the same period oftime.

According to several embodiments, ensemble system 102 can also be fullyoperational towards performing one or more other functions (e.g., fullypowered on, fully executed, etc.) while also performing the variousoperations described herein. It should be appreciated that suchsimultaneous multi-operational execution is beyond the capability of ahuman mind. It should also be appreciated that ensemble system 102 caninclude information that is impossible to obtain manually by an entity,such as a human user. For example, the type, amount, or variety ofinformation included in ensemble system 102, ensemble component 108,score component 110, quantum computing component 202, classicalcomputing component 204, trainer component 206, and/or boost component208 can be more complex than information obtained manually by a humanuser.

FIG. 9A illustrates a flow diagram of an example, non-limitingcomputer-implemented method 900 a that can facilitate a classical andquantum ensemble artificial intelligence (AI) model in accordance withone or more embodiments described herein. Repetitive description of likeelements and/or processes employed in respective embodiments is omittedfor sake of brevity.

In some embodiments, at 902 a, computer-implemented method 900 a cancomprise computing (e.g., via ensemble system 102, quantum computingcomponent 202, etc.) a quantum kernel (e.g., a quantum kernel matrix).For example, ensemble system 102 and/or quantum computing component 202can compute a quantum kernel matrix using a quantum kernel library.

In some embodiments, at 904 a, computer-implemented method 900 a cancomprise exporting (e.g., via ensemble system 102, quantum computingcomponent 202, classical computing component 204, etc.) the quantumkernel (e.g., quantum kernel matrix) to a classical system (e.g.,classical computing component 204).

In some embodiments, at 906 a, computer-implemented method 900 a cancomprise computing (e.g., via ensemble system 102, classical computingcomponent 204, etc.) a classical kernel and/or one or more supportvectors. For example, ensemble system 102 and/or classical computingcomponent 204 can employ a radial basis function (RBF) kernel to computesuch a classical kernel and/or support vector(s).

In some embodiments, at 908 a, computer-implemented method 900 a cancomprise boosting (e.g., via ensemble system 102, ensemble component108, boost component 208, etc.) one or more classical AI models and/orone or more quantum AI models. For example, ensemble system 102 and/orboost component 208 can employ a boosting technique (e.g., a boostingalgorithm such as, for instance, algorithm 300) to boost one or moreclassical AI models and/or one or more quantum AI models. In thisexample, ensemble system 102 and/or boost component 208 can boost one ormore classical AI models and/or one or more quantum AI models using thequantum kernel (e.g., quantum kernel matrix) computed at step 902 a asdescribed above.

In some embodiments, at 910 a, computer-implemented method 900 a cancomprise generating (e.g., via ensemble system 102, ensemble component108, etc.) an ensemble AI model comprising one or more classical AImodels and one or more quantum AI models.

In some embodiments, at 912 a, computer-implemented method 900 a cancomprise computing (e.g., via ensemble system 102, score component 110,etc.) probability scores of the classical AI models, the quantum AImodels, a boosted classical AI model, and/or a boosted quantum AI model.

In some embodiments, at 914 a, computer-implemented method 900 a cancomprise computing (e.g., via ensemble system 102, quantum computingcomponent 202, etc.) the dot product between unknown and support vectorscorresponding to one or more quantum AI models and/or one or moreboosted quantum AI models.

In some embodiments, at 916 a, computer-implemented method 900 a cancomprise combining (e.g., via ensemble system 102, ensemble component108, score component 110, etc.) probability scores of the classical AImodels, the quantum AI models, the boosted classical AI model, and/orthe boosted quantum AI model using a weighting scheme (e.g., asdescribed above with reference to FIGS. 3, 4, and 5 ).

FIG. 9B illustrates a flow diagram of an example, non-limitingcomputer-implemented method 900 b that can facilitate a classical andquantum ensemble artificial intelligence (AI) model in accordance withone or more embodiments described herein. Repetitive description of likeelements and/or processes employed in respective embodiments is omittedfor sake of brevity.

In some embodiments, at 902 b, computer-implemented method 900 b cancomprise generating, by a system (e.g., via ensemble system 102,ensemble component 108, boost component 208, etc.) operatively coupledto a processor (e.g., processor 106), an ensemble artificialintelligence model comprising a classical artificial intelligence model(e.g., a single classical AI model, a boosted classical AI model, etc.)and a quantum artificial intelligence model (e.g., a single quantum AImodel, a boosted classical AI model, etc.).

In some embodiments, at 904 b, computer-implemented method 900 b cancomprise computing, by the system (e.g., via ensemble system 102, scorecomponent 110, etc.), probability scores of a dataset based on theensemble artificial intelligence model.

For simplicity of explanation, the computer-implemented methodologiesare depicted and described as a series of acts. It is to be understoodand appreciated that the subject innovation is not limited by the actsillustrated and/or by the order of acts, for example acts can occur invarious orders and/or concurrently, and with other acts not presentedand described herein. Furthermore, not all illustrated acts can berequired to implement the computer-implemented methodologies inaccordance with the disclosed subject matter. In addition, those skilledin the art will understand and appreciate that the computer-implementedmethodologies could alternatively be represented as a series ofinterrelated states via a state diagram or events. Additionally, itshould be further appreciated that the computer-implementedmethodologies disclosed hereinafter and throughout this specificationare capable of being stored on an article of manufacture to facilitatetransporting and transferring such computer-implemented methodologies tocomputers. The term article of manufacture, as used herein, is intendedto encompass a computer program accessible from any computer-readabledevice or storage media.

In order to provide a context for the various aspects of the disclosedsubject matter, FIG. 10 as well as the following discussion are intendedto provide a general description of a suitable environment in which thevarious aspects of the disclosed subject matter can be implemented. FIG.10 illustrates a block diagram of an example, non-limiting operatingenvironment in which one or more embodiments described herein can befacilitated. Repetitive description of like elements employed in otherembodiments described herein is omitted for sake of brevity.

With reference to FIG. 10 , a suitable operating environment 1000 forimplementing various aspects of this disclosure can also include acomputer 1012. The computer 1012 can also include a processing unit1014, a system memory 1016, and a system bus 1018. The system bus 1018couples system components including, but not limited to, the systemmemory 1016 to the processing unit 1014. The processing unit 1014 can beany of various available processors. Dual microprocessors and othermultiprocessor architectures also can be employed as the processing unit1014. The system bus 1018 can be any of several types of busstructure(s) including the memory bus or memory controller, a peripheralbus or external bus, and/or a local bus using any variety of availablebus architectures including, but not limited to, Industrial StandardArchitecture (ISA), Micro-Channel Architecture (MSA), Extended ISA(EISA), Intelligent Drive Electronics (IDE), VESA Local Bus (VLB),Peripheral Component Interconnect (PCI), Card Bus, Universal Serial Bus(USB), Advanced Graphics Port (AGP), Firewire (IEEE 1394), and SmallComputer Systems Interface (SCSI).

The system memory 1016 can also include volatile memory 1020 andnonvolatile memory 1022. The basic input/output system (BIOS),containing the basic routines to transfer information between elementswithin the computer 1012, such as during start-up, is stored innonvolatile memory 1022. Computer 1012 can also includeremovable/non-removable, volatile/non-volatile computer storage media.FIG. 10 illustrates, for example, a disk storage 1024. Disk storage 1024can also include, but is not limited to, devices like a magnetic diskdrive, floppy disk drive, tape drive, Jaz drive, Zip drive, LS-100drive, flash memory card, or memory stick. The disk storage 1024 alsocan include storage media separately or in combination with otherstorage media. To facilitate connection of the disk storage 1024 to thesystem bus 1018, a removable or non-removable interface is typicallyused, such as interface 1026. FIG. 10 also depicts software that acts asan intermediary between users and the basic computer resources describedin the suitable operating environment 1000. Such software can alsoinclude, for example, an operating system 1028. Operating system 1028,which can be stored on disk storage 1024, acts to control and allocateresources of the computer 1012.

System applications 1030 take advantage of the management of resourcesby operating system 1028 through program modules 1032 and program data1034, e.g., stored either in system memory 1016 or on disk storage 1024.It is to be appreciated that this disclosure can be implemented withvarious operating systems or combinations of operating systems. A userenters commands or information into the computer 1012 through inputdevice(s) 1036. Input devices 1036 include, but are not limited to, apointing device such as a mouse, trackball, stylus, touch pad, keyboard,microphone, joystick, game pad, satellite dish, scanner, TV tuner card,digital camera, digital video camera, web camera, and the like. Theseand other input devices connect to the processing unit 1014 through thesystem bus 1018 via interface port(s) 1038. Interface port(s) 1038include, for example, a serial port, a parallel port, a game port, and auniversal serial bus (USB). Output device(s) 1040 use some of the sametype of ports as input device(s) 1036. Thus, for example, a USB port canbe used to provide input to computer 1012, and to output informationfrom computer 1012 to an output device 1040. Output adapter 1042 isprovided to illustrate that there are some output devices 1040 likemonitors, speakers, and printers, among other output devices 1040, whichrequire special adapters. The output adapters 1042 include, by way ofillustration and not limitation, video and sound cards that provide ameans of connection between the output device 1040 and the system bus1018. It should be noted that other devices and/or systems of devicesprovide both input and output capabilities such as remote computer(s)1044.

Computer 1012 can operate in a networked environment using logicalconnections to one or more remote computers, such as remote computer(s)1044. The remote computer(s) 1044 can be a computer, a server, a router,a network PC, a workstation, a microprocessor based appliance, a peerdevice or other common network node and the like, and typically can alsoinclude many or all of the elements described relative to computer 1012.For purposes of brevity, only a memory storage device 1046 isillustrated with remote computer(s) 1044. Remote computer(s) 1044 islogically connected to computer 1012 through a network interface 1048and then physically connected via communication connection 1050. Networkinterface 1048 encompasses wire and/or wireless communication networkssuch as local-area networks (LAN), wide-area networks (WAN), cellularnetworks, etc. LAN technologies include Fiber Distributed Data Interface(FDDI), Copper Distributed Data Interface (CDDI), Ethernet, Token Ringand the like. WAN technologies include, but are not limited to,point-to-point links, circuit switching networks like IntegratedServices Digital Networks (ISDN) and variations thereon, packetswitching networks, and Digital Subscriber Lines (DSL). Communicationconnection(s) 1050 refers to the hardware/software employed to connectthe network interface 1048 to the system bus 1018. While communicationconnection 1050 is shown for illustrative clarity inside computer 1012,it can also be external to computer 1012. The hardware/software forconnection to the network interface 1048 can also include, for exemplarypurposes only, internal and external technologies such as, modemsincluding regular telephone grade modems, cable modems and DSL modems,ISDN adapters, and Ethernet cards.

The present invention may be a system, a method, an apparatus and/or acomputer program product at any possible technical detail level ofintegration. The computer program product can include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention. The computer readable storage medium can be atangible device that can retain and store instructions for use by aninstruction execution device. The computer readable storage medium canbe, for example, but is not limited to, an electronic storage device, amagnetic storage device, an optical storage device, an electromagneticstorage device, a semiconductor storage device, or any suitablecombination of the foregoing. A non-exhaustive list of more specificexamples of the computer readable storage medium can also include thefollowing: a portable computer diskette, a hard disk, a random accessmemory (RAM), a read-only memory (ROM), an erasable programmableread-only memory (EPROM or Flash memory), a static random access memory(SRAM), a portable compact disc read-only memory (CD-ROM), a digitalversatile disk (DVD), a memory stick, a floppy disk, a mechanicallyencoded device such as punch-cards or raised structures in a groovehaving instructions recorded thereon, and any suitable combination ofthe foregoing. A computer readable storage medium, as used herein, isnot to be construed as being transitory signals per se, such as radiowaves or other freely propagating electromagnetic waves, electromagneticwaves propagating through a waveguide or other transmission media (e.g.,light pulses passing through a fiber-optic cable), or electrical signalstransmitted through a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network can comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device. Computer readable programinstructions for carrying out operations of the present invention can beassembler instructions, instruction-set-architecture (ISA) instructions,machine instructions, machine dependent instructions, microcode,firmware instructions, state-setting data, configuration data forintegrated circuitry, or either source code or object code written inany combination of one or more programming languages, including anobject oriented programming language such as Smalltalk, C++, or thelike, and procedural programming languages, such as the “C” programminglanguage or similar programming languages. The computer readable programinstructions can execute entirely on the user's computer, partly on theuser's computer, as a stand-alone software package, partly on the user'scomputer and partly on a remote computer or entirely on the remotecomputer or server. In the latter scenario, the remote computer can beconnected to the user's computer through any type of network, includinga local area network (LAN) or a wide area network (WAN), or theconnection can be made to an external computer (for example, through theInternet using an Internet Service Provider). In some embodiments,electronic circuitry including, for example, programmable logiccircuitry, field-programmable gate arrays (FPGA), or programmable logicarrays (PLA) can execute the computer readable program instructions byutilizing state information of the computer readable programinstructions to personalize the electronic circuitry, in order toperform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions. These computer readable programinstructions can be provided to a processor of a general purposecomputer, special purpose computer, or other programmable dataprocessing apparatus to produce a machine, such that the instructions,which execute via the processor of the computer or other programmabledata processing apparatus, create means for implementing thefunctions/acts specified in the flowchart and/or block diagram block orblocks. These computer readable program instructions can also be storedin a computer readable storage medium that can direct a computer, aprogrammable data processing apparatus, and/or other devices to functionin a particular manner, such that the computer readable storage mediumhaving instructions stored therein comprises an article of manufactureincluding instructions which implement aspects of the function/actspecified in the flowchart and/or block diagram block or blocks. Thecomputer readable program instructions can also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational acts to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams can represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the blocks can occur out of theorder noted in the Figures. For example, two blocks shown in successioncan, in fact, be executed substantially concurrently, or the blocks cansometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

While the subject matter has been described above in the general contextof computer-executable instructions of a computer program product thatruns on a computer and/or computers, those skilled in the art willrecognize that this disclosure also can or can be implemented incombination with other program modules. Generally, program modulesinclude routines, programs, components, data structures, etc. thatperform particular tasks and/or implement particular abstract datatypes. Moreover, those skilled in the art will appreciate that theinventive computer-implemented methods can be practiced with othercomputer system configurations, including single-processor ormultiprocessor computer systems, mini-computing devices, mainframecomputers, as well as computers, hand-held computing devices (e.g., PDA,phone), microprocessor-based or programmable consumer or industrialelectronics, and the like. The illustrated aspects can also be practicedin distributed computing environments in which tasks are performed byremote processing devices that are linked through a communicationsnetwork. However, some, if not all aspects of this disclosure can bepracticed on stand-alone computers. In a distributed computingenvironment, program modules can be located in both local and remotememory storage devices.

As used in this application, the terms “component,” “system,”“platform,” “interface,” and the like, can refer to and/or can include acomputer-related entity or an entity related to an operational machinewith one or more specific functionalities. The entities disclosed hereincan be either hardware, a combination of hardware and software,software, or software in execution. For example, a component can be, butis not limited to being, a process running on a processor, a processor,an object, an executable, a thread of execution, a program, and/or acomputer. By way of illustration, both an application running on aserver and the server can be a component. One or more components canreside within a process and/or thread of execution and a component canbe localized on one computer and/or distributed between two or morecomputers. In another example, respective components can execute fromvarious computer readable media having various data structures storedthereon. The components can communicate via local and/or remoteprocesses such as in accordance with a signal having one or more datapackets (e.g., data from one component interacting with anothercomponent in a local system, distributed system, and/or across a networksuch as the Internet with other systems via the signal). As anotherexample, a component can be an apparatus with specific functionalityprovided by mechanical parts operated by electric or electroniccircuitry, which is operated by a software or firmware applicationexecuted by a processor. In such a case, the processor can be internalor external to the apparatus and can execute at least a part of thesoftware or firmware application. As yet another example, a componentcan be an apparatus that provides specific functionality throughelectronic components without mechanical parts, wherein the electroniccomponents can include a processor or other means to execute software orfirmware that confers at least in part the functionality of theelectronic components. In an aspect, a component can emulate anelectronic component via a virtual machine, e.g., within a cloudcomputing system.

In addition, the term “or” is intended to mean an inclusive “or” ratherthan an exclusive “or.” That is, unless specified otherwise, or clearfrom context, “X employs A or B” is intended to mean any of the naturalinclusive permutations. That is, if X employs A; X employs B; or Xemploys both A and B, then “X employs A or B” is satisfied under any ofthe foregoing instances. Moreover, articles “a” and “an” as used in thesubject specification and annexed drawings should generally be construedto mean “one or more” unless specified otherwise or clear from contextto be directed to a singular form. As used herein, the terms “example”and/or “exemplary” are utilized to mean serving as an example, instance,or illustration. For the avoidance of doubt, the subject matterdisclosed herein is not limited by such examples. In addition, anyaspect or design described herein as an “example” and/or “exemplary” isnot necessarily to be construed as preferred or advantageous over otheraspects or designs, nor is it meant to preclude equivalent exemplarystructures and techniques known to those of ordinary skill in the art.

As it is employed in the subject specification, the term “processor” canrefer to substantially any computing processing unit or devicecomprising, but not limited to, single-core processors;single-processors with software multithread execution capability;multi-core processors; multi-core processors with software multithreadexecution capability; multi-core processors with hardware multithreadtechnology; parallel platforms; and parallel platforms with distributedshared memory. Additionally, a processor can refer to an integratedcircuit, an application specific integrated circuit (ASIC), a digitalsignal processor (DSP), a field programmable gate array (FPGA), aprogrammable logic controller (PLC), a complex programmable logic device(CPLD), a discrete gate or transistor logic, discrete hardwarecomponents, or any combination thereof designed to perform the functionsdescribed herein. Further, processors can exploit nano-scalearchitectures such as, but not limited to, molecular and quantum-dotbased transistors, switches and gates, in order to optimize space usageor enhance performance of user equipment. A processor can also beimplemented as a combination of computing processing units. In thisdisclosure, terms such as “store,” “storage,” “data store,” datastorage,” “database,” and substantially any other information storagecomponent relevant to operation and functionality of a component areutilized to refer to “memory components,” entities embodied in a“memory,” or components comprising a memory. It is to be appreciatedthat memory and/or memory components described herein can be eithervolatile memory or nonvolatile memory, or can include both volatile andnonvolatile memory. By way of illustration, and not limitation,nonvolatile memory can include read only memory (ROM), programmable ROM(PROM), electrically programmable ROM (EPROM), electrically erasable ROM(EEPROM), flash memory, or nonvolatile random access memory (RAM) (e.g.,ferroelectric RAM (FeRAM). Volatile memory can include RAM, which canact as external cache memory, for example. By way of illustration andnot limitation, RAM is available in many forms such as synchronous RAM(SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rateSDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM),direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), andRambus dynamic RAM (RDRAM). Additionally, the disclosed memorycomponents of systems or computer-implemented methods herein areintended to include, without being limited to including, these and anyother suitable types of memory.

What has been described above include mere examples of systems andcomputer-implemented methods. It is, of course, not possible to describeevery conceivable combination of components or computer-implementedmethods for purposes of describing this disclosure, but one of ordinaryskill in the art can recognize that many further combinations andpermutations of this disclosure are possible. Furthermore, to the extentthat the terms “includes,” “has,” “possesses,” and the like are used inthe detailed description, claims, appendices and drawings such terms areintended to be inclusive in a manner similar to the term “comprising” as“comprising” is interpreted when employed as a transitional word in aclaim.

The descriptions of the various embodiments have been presented forpurposes of illustration, but are not intended to be exhaustive orlimited to the embodiments disclosed. Many modifications and variationswill be apparent to those of ordinary skill in the art without departingfrom the scope and spirit of the described embodiments. The terminologyused herein was chosen to best explain the principles of theembodiments, the practical application or technical improvement overtechnologies found in the marketplace, or to enable others of ordinaryskill in the art to understand the embodiments disclosed herein.

What is claimed is:
 1. A system, comprising: a memory that storescomputer executable components; and a processor that executes thecomputer executable components stored in the memory, wherein thecomputer executable components comprise: an ensemble component thatgenerates an ensemble artificial intelligence model comprising aclassical artificial intelligence model and a quantum artificialintelligence model; and a score component that computes probabilityscores of a dataset based on the ensemble artificial intelligence model.2. The system of claim 1, wherein at least one of the classicalartificial intelligence model or the quantum artificial intelligencemodel comprises a boosted artificial intelligence model comprising twoor more artificial intelligence models, thereby facilitating at leastone of improved probability scores of the dataset or improved processingperformance of the processor.
 3. The system of claim 1, wherein thecomputer executable components further comprise: a quantum computingcomponent that computes at least one of a quantum kernel or one or morequantum support vectors.
 4. The system of claim 1, wherein the computerexecutable components further comprise: a classical computing componentthat computes at least one of a classical kernel or one or moreclassical support vectors, and wherein the classical computing componentcomputes the one or more classical support vectors based on at least oneof the classical kernel or a quantum kernel.
 5. The system of claim 1,wherein the computer executable components further comprise: a trainercomponent that trains the classical artificial intelligence model basedon training data and trains the quantum artificial intelligence modelbased on a subset of the training data.
 6. The system of claim 1,wherein the computer executable components further comprise: a boostcomponent that generates at least one of a boosted classical artificialintelligence model comprising two or more classical artificialintelligence models or a boosted quantum artificial intelligence modelcomprising two or more quantum artificial intelligence models.
 7. Thesystem of claim 1, wherein the score component further computesprobability scores of the dataset based on at least one of the classicalartificial intelligence model or the quantum artificial intelligencemodel.
 8. A computer-implemented method, comprising: generating, by asystem operatively coupled to a processor, an ensemble artificialintelligence model comprising a classical artificial intelligence modeland a quantum artificial intelligence model; and computing, by thesystem, probability scores of a dataset based on the ensemble artificialintelligence model.
 9. The computer-implemented method of claim 8,wherein at least one of the classical artificial intelligence model orthe quantum artificial intelligence model comprises a boosted artificialintelligence model comprising two or more artificial intelligencemodels, thereby facilitating at least one of improved probability scoresof the dataset or improved processing performance of the processor. 10.The computer-implemented method of claim 8, further comprising:computing, by the system, at least one of a quantum kernel or one ormore quantum support vectors.
 11. The computer-implemented method ofclaim 8, further comprising: computing, by the system, at least one of aclassical kernel or one or more classical support vectors; andcomputing, by the system, the one or more classical support vectorsbased on at least one of the classical kernel or a quantum kernel. 12.The computer-implemented method of claim 8, further comprising:training, by the system, the classical artificial intelligence modelbased on training data; and training, by the system, the quantumartificial intelligence model based on a subset of the training data.13. The computer-implemented method of claim 8, further comprising:generating, by the system, at least one of a boosted classicalartificial intelligence model comprising two or more classicalartificial intelligence models or a boosted quantum artificialintelligence model comprising two or more quantum artificialintelligence models.
 14. The computer-implemented method of claim 8,further comprising: computing, by the system, probability scores of thedataset based on at least one of the classical artificial intelligencemodel or the quantum artificial intelligence model.
 15. A computerprogram product facilitating a classical and quantum ensemble artificialintelligence model, the computer program product comprising a computerreadable storage medium having program instructions embodied therewith,the program instructions executable by a processor to cause theprocessor to: generate, by the processor, an ensemble artificialintelligence model comprising a classical artificial intelligence modeland a quantum artificial intelligence model; and compute, by the system,probability scores of a dataset based on the ensemble artificialintelligence model.
 16. The computer program product of claim 15,wherein at least one of the classical artificial intelligence model orthe quantum artificial intelligence model comprises a boosted artificialintelligence model comprising two or more artificial intelligencemodels.
 17. The computer program product of claim 15, wherein, theprogram instructions are further executable by the processor to causethe processor to: compute, by the processor, at least one of a quantumkernel or one or more quantum support vectors.
 18. The computer programproduct of claim 15, wherein, the program instructions are furtherexecutable by the processor to cause the processor to: compute, by theprocessor, at least one of a classical kernel or one or more classicalsupport vectors; and compute, by the processor, the one or moreclassical support vectors based on at least one of the classical kernelor a quantum kernel.
 19. The computer program product of claim 15,wherein, the program instructions are further executable by theprocessor to cause the processor to: train, by the processor, theclassical artificial intelligence model based on training data; andtrain, by the processor, the quantum artificial intelligence model basedon a subset of the training data.
 20. The computer program product ofclaim 15, wherein, the program instructions are further executable bythe processor to cause the processor to: generate, by the processor, atleast one of a boosted classical artificial intelligence modelcomprising two or more classical artificial intelligence models or aboosted quantum artificial intelligence model comprising two or morequantum artificial intelligence models.